It has been shown [1]} that if there exists a strong solution \(u \in C([0,T];L^2_x)\)  for given initial data \(\overline{u}\) , such that
\(\int _0^T \Vert \nabla u(t) + \nabla u(t)^T\Vert _{L^\infty _x} \, dt < \infty ,\) 
